the speed limit on the highway is 60 miles per hour. Mr.Erikson is driving at 53 miles per hour. Write and solve an inequality to find how much faster Mr. Erikson can drive while still obeying the speed limit​

Answer:

A

Step-by-step explanation:

1) Count the numbers larger than 5

(6,7,8,9,10)

2) Put it over a fraction

5/10

3)Simplify

1/2

for (A^x)^y = A^xy

Thus for (3^-5)^-2 = 3^n

n = -5×-2 =10

Answer:

n=10

Step-by-step explanation:

We know that a^b^c = a^(b*c)

3 ^-5^-2 = 3^(-5*-2)

             = 3^(10)

3^n = 3^10

n = 10

Answer:

1/9

Step-by-step explanation:

Separate the fraction (1/9) from the variable x:

y = (1/9)x.

1/9 is the constant of proportionality.

The constant of proportionality in the equation y=x/9 is 1/9.

A constant of proportionality is a constant that is multiplied by a variable to make two variables equal.

The equation is given as:

y=x/9

Observe the given equation. Here, we can see that x and y are variables.

This means that 1/9 is the constant of proportionality.

A constant of proportionality is a constant that is multiplied by a variable to make two variables equal.

Therefore, the constant of proportionality is found. The value of the constant of proportionality is 1/9.

Therefore, we have found the constant of proportionality in the equation y=x/9 is 1/9.

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Answer:

b

Step-by-step explanation:

104.4...............................:::::::

Answer:

a lot

Step-by-step explanation:

Answer: The table that represents a function is table A

Step-by-step explanation: This is because every time the input goes down once with a change of output, where as a nonlinear function doesn't do this

Answer:

Mean : 95

Median : 85

Mode : 90

Part B : Impossible

Step-by-step explanation:

We can make an equation to find the mean using the first 5 history test scores.

[tex]85=\frac{80+75+90+75+95+n}{6} \\ \\ 85=\frac{415+n}{6} \\ \\ 510=415+n \\ \\ n=95[/tex]

So a 95 would be needed to have a mean of 85.

Next, the median.

First, we sort the first 5 history scores from least to greatest.

We get 75, 75, 80, 90, 95.

Since, 80 is the middle value, it will be used in the calculation of the median.

We can make an equation with this.

[tex]82.5=\frac{80+n}{2} \\ \\ 165=80+n \\ \\ n=85[/tex]

So a score a 85 would be needed to have a median of 82.5

Thirdly, the mode.

Since 90 is already in the set once, we can just have Maliah score another 90 to make 90 the mode (with the exception of 75 of course).

Finally, Part B.

We can use the equation we had for the first mean calculation but change 85 to 90.

[tex]90=\frac{80+75+90+75+95+n}{6} \\ \\ 90=\frac{415+n}{6} \\ \\ 540=415+n \\ \\ n=125[/tex]

So Maliah would need a score of 125 to make her mean score 90, but since the range is only from 0-100, it is impossible.

Answer:

204

Step-by-step explanation:

To find the volume of a rectanguar prism, you must multiply legnth x width x height to get the volume.

Before we multiply, first lets convert the fractions into improper fractions to make multiplying a little easier.

6 3/8 = 51/8

10 2/3 = 32/3

Now, we multiply.

[To multiply fractions, multiply the numerators and denominators.]

51/8 x 32/3

51 x 32 = 1632

8 x 3 = 24

1632/24 = 68

Now that we've multiplyed the length and height, multiply 68 by the width, 3.

68 x 3 = 204

Therefore, the volume of the rectangular prism is 204. I hope this helps!

About 204 inches.

Hope this helps!

Answer:

20

Step-by-step explanation:

This reads mathematically exactly how it is stated in words.  The word "is" means =, the word "of" means multiply, and "what number" is x.  Therefore, the equation from that looks like this:  16 = .80x.  Don't forget that you cannot use a percent in an equation without first changing it to its decimal equivalency.  Solve that for x by dividing both sides by .80 to get that x = 20

The number that when 80 % is found of it, would give the result of 16 is the number 20.

To determine the number that 16 is 80% of, you can set up an equation using algebra.

Let's represent the unknown number with the variable "x." The equation can be written as:

16 = 80% of x

To solve for "x," we need to isolate it on one side of the equation.

Since 80% is equivalent to 0.8 as a decimal, we can rewrite the equation as:

16 = 0.8x

To solve for "x," divide both sides of the equation by 0.8:

16 / 0.8 = 0.8x / 0.8

Simplifying the equation:

20 = x

Therefore, the number that 16 is 80% of is 20.

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For this case we have the following functions:

[tex]f (x) = x + 7\\g (x) = \frac {1} {x}[/tex]

We must find [tex](f_ {0} g) (x):[/tex]

By definition:

[tex](f_ {0} g) (x) = f (g (x))[/tex]

So, evaluating g(x) in f(x) we have:

[tex](f_ {0} g) (x) = f (g (x)) = \frac {1} {x} +7[/tex]

ANswer:

[tex]\frac {1} {x} +7[/tex]

Option D

Answer:

∠ADC and ∠BDC are supplementary

A pair of complementary angles is angles ACD and DCB.

<ADC and <BDC are supplementary angles

<ACD and <BCD are complementary angles)

Complementary Angles: Two angles that add up to 90 degrees, complementing each other to form a right angle, e.g., 30 and 60 degrees.

Supplementary Angles: Two angles that add up to 180 degrees, forming a straight line, e.g., 120 and 60 degrees.

From the figure

ED is a ray that bisects AB and <ACB

<ACB is 90⁰(given)

<ADC + <BDC = 180( linear angles)

Linear angles are supplementary

Therefore

<ADC and <BDC are supplementary angles

Since <ACB = 90⁰

ED is a bisector

Therefore

<ACD + <BCD = 90⁰

<ACD and <BCD are complementary angles)

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You would get paid $1.25 per hour, you divide 50 by 40 and get 1.25. Hope this helps ʅ（◞‿◟）ʃ

the answers is 1.25

enjoy good grades!!!!!

It’s C or 34+24=58 so the answer is C

It is c 58 your welcome

Answer:

Step-by-step explanation:

Look at the picture.

ΔADC and ΔCDB are similar (AAA). Therefore corresponding sides are in proportion

[tex]\dfrac{15}{x}=\dfrac{x}{20-15}\\\\\dfrac{15}{x}=\dfrac{x}{5}[/tex]

cross multiply

[tex]x^2=(15)(5)\\\\x^2=75\to x=\sqrt{75}\\\\x=\sqrt{25\cdot5}\\\\x=\sqrt{25}\cdot\sqrt5\\\\x=5\sqrt5[/tex]

Answer:

13/12

Step-by-step explanation:

B - 7/4 = -2/3

B = -2/3 + 7/4

B = 13/12

f(x) is linear

g(x) is exponential

Answer: linear, exponential

Step-by-step explanation:

f(x) the blue line has a constant slope so is a line (linear).

g(x) the red line has an asymptote at x = 0 and has an exponential rate/slope so is exponential.

1. 10x+5=35

2. 5x+10=35

3. 35x+5=10

B. Interquartile Range

(5k^2)^3 simplifies to 125k^6.

To simplify the expression (5k^2)^3, we can apply the exponent rule. The rule states that when raising a power to another power, we multiply the exponents together.

In this case, we have (5k^2)^3. To simplify, we raise both the base, 5, and the exponent, k^2, to the third power.

First, let's raise the base, 5, to the third power:
5^3 = 5 x 5 x 5 = 125

Next, let's raise the exponent, k^2, to the third power:
(k^2)^3 = k^(2 x 3) = k^6

Therefore, (5k^2)^3 simplifies to 125k^6.

Answer:

b

Step-by-step explanation:

to find volume you have to multiply 12, 6 and 8.5

if it is right rate and thanks me so others know it is right

Answer:

[tex]v = \frac{i \: \times w \ \times h}{3} \\ \: \: \: \: = \frac{8.5 \times 6 \times 12}{3} \\ \: \: \: \: = 204 {in}^{3} [/tex]

Answer D is correct.

Answer: The answer is 9 i am 100% sure

Step-by-step explanation:

It would be

B.9 I hope this helps

Answer:

The correct answer is option D.  790 m²

Step-by-step explanation:

Formula:-

Area of triangle = bh/2

Area of rectangle = bh

where b - Base and h - Height

To find the area of prism

Area of prism = Base area  + side rectangle area + side triangle area

 = (16 * 11)  + (2 * 11 * 17) + (2 * 16 * 15 /2)

 = 176 + 374 + 240

 = 790 m²

Therefore the correct answer is option D.  790 m²

The surface area of the triangular prism is 790m². ( option D)

A triangular prism is a type of prism with triangular base. The surface area of a prism is expressed as ;

SA = 2B + ph

where , B is the base area and p is the perimeter of the base.

Base area = 1/2bh

where b is the base and h is the height

= 1/2 × 16 × 15

= 8 × 15

= 120m²

Perimeter = 17 + 16 + 17 = 50m²

Surface area = 2 × 120 + 50 × 11

= 240 + 550

= 790 m²

Therefore, the surface area of the prism is 790m²

Answer:

27.5 square yards

Step-by-step explanation:

So, we have two shapes connected together and we want to know the combined area of the two.  All we have to do is find out the area of each one, then add the results.

First, the rectangle:

The area of a rectangle is the base multiplied by the height, so

A = 6 x 4 = 24 square yards

Then, the half-circle.

We know the area of a circle is calculated with A = π * r², so the area of a half circle will be A = (π * r²)/2.

We know the circle has a diameter of 3 yards because the wall next to it is also 3 yards and the whole structure is 6 yards wide, so...

A = (π (1.5)²)/2 = 2.25 π / 2 = 3.53 square yards

Overall, we have

Area of the rectangle: 24 square yards

Area of the half-circle: 3.53 square yards

Total: 27.53 square yards, rounded to the tenth: 27.5 square yards.

Answer:

27.5 yards^2

Step-by-step explanation:

We are given a figure which comprises of two shapes: a rectangle and a semicircle and we are to find the area of this composite figure.

We know that the area of these two shapes is given by the following formulas so we will put in the given values to get:

Area of rectangle = [tex]length \times width[/tex] = [tex]6 \times 4[/tex] = 24 yd^2

Area of semi-circle = [tex]\frac{\pi r^2}{2}[/tex] = [tex]\frac{3.14 \times 1.5^2}{2}[/tex] = 3.53 yd^2

Area of composite figure = [tex]24+3.53[/tex] = 27.5 yards^2

Answer:

Width is 5 and length is 7

Step-by-step explanation:

You can solve the equation using the distributive property and inverse operations.

2x +2(x+2)=24

2x + 2x + 4 = 24

4x + 4 = 24

4x = 20

X = 5

This means the width is 5 and the length is 7.

The width of the rectangle is 5 inches and its length is 7 inches.

The given equation 2x + 2(x + 2) = 24 represents the situation with a rectangle's length being 2 inches more than its width and the perimeter of the rectangle being 24 inches. To find the value of x from the set {1, 3, 5, 7} that holds true for the equation, we can substitute each value into the equation and solve for x. By trying each value, we find that x = 5 holds true for the equation.

Therefore, the width of the rectangle is 5 inches and since the length is 2 inches more than the width, the length would be 7 inches.

Answer:

3.64

Step-by-step explanation:

65 + 66 + 70 + 58 + 61 = 319

319/5 = 63.8

65 - 63.8 = |1.2|

66 - 63.8 = |2.2|

70 - 63.8 = |6.2|

58 - 63.8 = |-5.8| = 5.8

61 - 63.8 = |-2.8| = 2.8

1.2 + 2.2 + 6.2 + 5.8 + 2.8 = 18.2

18.2/5 = 3.64

105 Degree

Because the angle x

Is the same angle of 105 in X to Y

Answer:

C

Step-by-step explanation:

Since DE and XY are parallel lines then

x and 105 are corresponding angles and congruent, hence

x = 105 → C

Answer:

Step-by-step explanation:

L is 2* W so L=2W

perimeter= 2w+2l

plug in whats given to get

perimeter=2w+4w   4w is because L is *2 of W so that makes L=2w

36=6w

36/6=6

6w/6=w

w=6

6*2=12=L

now we have 6*12=72=Area

Answer:

EF , HG , Parallel

Step-by-step explanation:

Here we are given a translated quadrilateral EFGH from Quadrilateral ABCD.

Also given that AB was parallel to DC.

Now we have to fill in the certain blanks.

Here EF is parallel to AB , As EFGH is a translated image of ABCD. And EF and AB are the corresponding sides.

Also HG is parallel to DC, EFGH is a translated image of ABCD.

Also we are given that AB is parallel to DC. Hence we have following results.

AB║DC

AB║EF

Hence CD║EF

also

CD ║HG

CD║EF

Hence we can come to conclusion that

EF║HG

Hence our answer will be

corresponding segments EF and HG are parallel to each other.

Answer:

Surface area = [tex]261.6cm^2[/tex]

Volume = [tex]281.2cm^3[/tex]

Step-by-step explanation:

To find the surface area of our cone, we are using the formula for the surface area of a cone:

[tex]A=\pir(r+\sqrt{h^2+r^2} )[/tex]

where

[tex]A[/tex] is the surface area

[tex]r[/tex] is the radius

[tex]h[/tex] is the height

Notice that the height, radius, and slant height make a right triangle, so to find the height, [tex]h[/tex], we can use the Pythagorean theorem:

[tex]s^2=r^2+h^2[/tex]

[tex]14^2=4.5^2+h^2[/tex]

[tex]196=20.25+h^2[/tex]

[tex]h^2=196-20.25[/tex]

[tex]h^2=175.75[/tex]

[tex]h=\sqrt{175.75}[/tex]

[tex]h=13.26[/tex] cm

We have all we need now to find the surface area of our cone:

[tex]A=\pir(r+\sqrt{h^2+r^2} )[/tex]

[tex]A=\pi(4.5)(4.5+\sqrt{13.26^2+4.5^2} )[/tex]

[tex]A=261.6cm^2[/tex]

Now, to find the volume of our cone, we are using the formula for the volume of a cone:

[tex]V=\frac{\pi r^2h}{3}[/tex]

where

[tex]V[/tex] is the volume

[tex]r[/tex] is the radius

[tex]h[/tex] is the height

Replacing values

[tex]V=\frac{\pi (4.5^2)(13.26)}{3}[/tex]

[tex]V=281.2cm^3[/tex]

We can conclude that the surface area of our cone is 261.6 square centimeters and its volume is 281.2 cubic centimeters.

Answer:

Surface area [tex]= 261.405 cm^2\\[/tex]

Volume of the cone [tex]= 177.19 cm^3\\[/tex]

Step-by-step explanation:

Slant height of cone [tex]= (r + \sqrt{r^2 + h^2}) \\[/tex]

Height of the cone will be derived from this slant height

[tex]14 = 4.5 + \sqrt{4.5^2 + h^2} \\9.5 = \sqrt{4.5^2 + h^2}\\90.25 = 20.25 + h^2\\h = 8.36\\[/tex]

Surface Area of Cone

[tex]= \pi r (r + l)\\= (3.14) (4.5) (4.5 + 14)\\= 261.405[/tex]

Volume of the cone

[tex]= \frac{1}{3} \pi r^2h\\= \frac{1}{3} (3.14)(4.5^2) (8.36)\\= 177.19 cm^3\\[/tex]

[tex]c. \: \frac{1}{b^{3} } [/tex]